Mathematical Definitions
For a given real field, we can say that the theory has a mass gap if the two-point function has the property
with being the lowest energy value in the spectrum of the Hamiltonian and thus the mass gap. This quantity, easy to generalize to other fields, is what is generally measured in lattice computations. It was proved in this way that Yang-Mills theory develops a mass gap. The corresponding time-ordered value, the propagator, will have the property
with the constant being finite. A typical example is offered by a free massive particle and, in this case, the constant has the value 1/m2. In the same limit, the propagator for a massless particle is singular.
Read more about this topic: Mass Gap
Famous quotes containing the words mathematical and/or definitions:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)